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Answer the following questions dealing with
trigonometric graphs.
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1. |
The temperature in an office is controlled by
an electronic thermostat. The temperatures vary
according to the sinusoidal function:
where y is the temperature (ºC) and x is the
time in hours past midnight.a.)
What is the temperature in the office at 9 A.M.
when employees come to work?
b.) What are the maximum and minimum
temperatures in the office?
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2. |
The number of hours of daylight measured in
one year in Ellenville can be modeled by a sinusoidal
function. During 2006, (not a leap year), the longest
day occurred on June 21 with 15.7 hours of daylight.
The shortest day of the year occurred on December 21 with
8.3 hours of daylight. Write a sinusoidal equation to
model the hours of daylight in Ellenville. |
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3. |
A pet store clerk
noticed that the population in the gerbil habitat varied
sinusoidally with respect to time, in days. He carefully
collected data and graphed his resulting equation. From
the graph, determine the amplitude, period, phase
shift and vertical shift. Write the equation of the graph.
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4. |
Given the following
equations, determine the amplitude, period, phase
shift, and vertical shift of each equation.
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Are these two equations equivalent?
Support your answer graphically and algebraically. |
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5. |
Environmentalists use sinusoidal functions to model
populations of predators and prey in the environment.
In a particular study, the population of rabbits was modeled
by the function
The population of wolves in
the same environmental area was modeled by the function
In each formula, x represents time in months.
Using the graphs of these two
equations, make a statement regarding the relationship
between the number of rabbits and the number of wolves in
this environmental area. |
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6. |
Write both a sine
and a cosine equation for the following graph.
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7. |
A team of biologists have discovered a new creature in
the rain forest. They note the temperature of the animal appears to vary sinusoidally over time. A maximum temperature of 125
° occurs 15 minutes after they
start their examination. A minimum temperature of 99
° occurs 28 minutes later. The
team would like to find a way to predict the animal’s temperature over
time in minutes. Your task is to help them by creating a graph of one
full period and an equation of temperature as a function over time in
minutes |
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8. |
The angle of inclination of the sun changes throughout the year.
This changing angle affects the heating and cooling of buildings.
The overhang of the roof of a house is designed to shade the windows for
cooling in the summer and allow the sun's rays to enter the house for
heating in the winter. The sun's angle of inclination at noon in
central New York state can be modeled by the formula:
where x is the number of days elapsed in the day
of the year, with January first represented by x = 1, January
second represented by x = 2, and so on.
Find the sun's angle of inclination at noon on
Valentine's Day.
Sketch a graph illustrating the changes in the sun's angle of
inclination throughout the year. On what date of the year is the
angle of inclination at noon the greatest in central New York state?
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